A remark on extension of order preserving operator inequality (Q2883207)

As a nice extension of \textit{T. Furuta}'s inequality [Proc. Am. Math. Soc. 101, No. 1, 85--88 (1987; Zbl 0721.47023)], the generalized Furuta inequality is a well-known operator inequality [Linear Algebra Appl. 219, 139--155 (1995; Zbl 0822.15008)]. It interpolates the Furuta and the so-called Ando-Hiai inequalities shown in [\textit{T. Ando} and \textit{F. Hiai}, Linear Algebra Appl. 197--198, 113--131 (1994; Zbl 0793.15011)]. Moreover, the generalized Furuta inequality has been extended by \textit{M. Uchiyama} [J. Math. Soc. Japan 55, No. 1, 197--207 (2003; Zbl 1036.47008)], who extended it to an operator inequality of three operators. Recently, \textit{T. Furuta} obtained another extension of the generalized inequality which is an operator inequality of several operators [J. Math. Inequal. 2, No. 4, 465--472 (2008; Zbl 1168.47016)], see also [\textit{C.-S. Yang} and \textit{Y.-Q. Wang}, J. Math. Inequal. 4, No. 3, 391--398 (2010; Zbl 1207.47015)]. In this paper, the authors obtain a further extension of the result by Yang and Wang under weaker assumptions.